Many Logics, One Methodology: A Plea for Logical Pluralism in Formalised Reasoning (preprint)

Problem
This preprint addresses the gap in the formalized reasoning literature regarding the integration of multiple non-classical logics within a unified framework. The authors critique the prevalent trend of logical imperialism, where a single foundational logic is rigidly adopted for large-scale theory development, which limits interdisciplinary collaboration and the reuse of logical frameworks. They advocate for logical pluralism, particularly in the context of modern proof assistants, to enhance the expressiveness and applicability of formal reasoning systems.

Method
The core technical contribution of this paper is the promotion of the LogiKEy methodology, which facilitates the embedding of various non-classical logics into classical higher-order logic (HOL). The authors argue for a meta-logical framework that supports logical pluralism at the object-logic level. They draw on computational metaphysics to substantiate their claims, suggesting that a pluralistic approach can better accommodate the diverse requirements of different domains in formal reasoning. The paper does not disclose specific architectures, loss functions, or training compute, as it primarily focuses on theoretical arguments rather than empirical evaluations.

Results
As a position statement, the paper does not present quantitative results or benchmark comparisons typical of empirical studies. Instead, it emphasizes the conceptual advantages of adopting a pluralistic approach to logic, arguing that it can lead to more robust and flexible reasoning systems. The authors suggest that the LogiKEy framework can enhance the interoperability of various logical systems, although no specific effect sizes or performance metrics are provided against named baselines.

Limitations
The authors acknowledge that their position is primarily theoretical and lacks empirical validation through case studies or quantitative analysis. They do not provide specific examples of how the LogiKEy methodology has been implemented or tested in practice, which could limit the applicability of their arguments. Additionally, the paper does not address potential challenges in reconciling different logics within a single framework, such as computational complexity or the potential for inconsistencies.

Why it matters
This work has significant implications for the development of formal reasoning systems, particularly in the context of proof assistants and knowledge representation. By advocating for logical pluralism, the authors encourage a shift away from monolithic logical frameworks, which can stifle innovation and interdisciplinary collaboration. The LogiKEy methodology could serve as a foundation for future research that seeks to integrate diverse logical systems, thereby enhancing the expressiveness and utility of formal reasoning in various applications, including artificial intelligence, computational linguistics, and knowledge representation.

Authors: Christoph Benzmüller, Daniel Kirchner, Luca Pasetto
Source: arXiv:2605.27246
URL: https://arxiv.org/abs/2605.27246v1